<h2>Problem 271</h2>
<div style="color:#666;font-size:80%;">02 January 2010</div><br />
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<P>
For a positive number <var>n</var>, define S(<var>n</var>) as the sum of the integers <var>x,</var> for which 1<img src='images/symbol_lt.gif' width='10' height='10' alt='&lt;' border='0' style='vertical-align:middle;' /><var>x</var><img src='images/symbol_lt.gif' width='10' height='10' alt='&lt;' border='0' style='vertical-align:middle;' /><var>n</var> and<BR /> <var>x</var><img src="" style="display:none;" alt="^(" /><sup>3</sup><img src="" style="display:none;" alt=")" /><img src='images/symbol_cong.gif' width='9' height='11' alt='&equiv;' border='0' style='vertical-align:middle;' />1 mod <var>n</var>.
</P>
<P>
When <var>n</var>=91, there are 8 possible values for <var>x</var>, namely : 9, 16, 22, 29, 53, 74, 79, 81.<BR />
Thus, S(91)=9+16+22+29+53+74+79+81=363.</P>
<P>
Find S(13082761331670030).
</P>

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